Proceedings of PACLIC 19, the 19th Asia-Pacific Conference on Language, Information and Computation.

Empirical Verification of Meaning-Game-based Generalizationof Centering Theory with Large Japanese Corpus
Shun SHIRAMATSU†
Kazunori KOMATANI†
Takashi MIYATA††{siramatu, komatani}@kuis.kyoto-u.ac.jp
miyata.t@aist.go.jp†††, ††^
Koiti HASIDA
Hiroshi G. OKUNO†
hasida.k@aist.go.jp
okuno@kuis.kyoto-u.ac.jp†Graduate Schoolof Informatics,
Kyoto University
Yoshida-Honmachi,
Sakyo-ku,
Kyoto 606-8501, Japan††CREST,
Japan Science andTechnology Agency (JST)Akihabara Dai-Building, SotoKanda 1-18-13, Chiyoda-ku,
Tokyo 101-0021, Japan†††ITRI, National Instituteof Advanced Industrial
Science and Technology (AIST)
Akihabara Dai-Building, SotoKanda 1-18-13, Chiyoda-ku,
Tokyo 101-0021, Japan

Abstract
Centering theory (Grosz et al., 1995) tries to explain relations among attention, anaphora, andcohesion. It has two theoretical limitations. The first is the lack of a principle behind these
discourse phenomena. The second is that the salience of discourse entities has not been
quantitatively defined, although it plays a critical role in this theory. Hasida et al. (1995, 1996)
propose the meaning game as a more principled model of intentional communication based on
game theory, and claim that it can derive centering theory. This claim, however, has not yet beenverified on the basis of substantial linguistic data. In this paper, we formulate salience as ameasurable quantity in terms of a reference probability. We also formulate preferences subsuming
centering theory under this quantitative formulation of salience. The preferences are derived fromthe meaning game and entail more general predictions than those of conventional centering theory.
These formulations overcome the above limitations of centering theory. By following them, we
empirically verify our generalization with a large Japanese corpus. The experimental results showthat there is positive correlation between the salience (reference probability) of an entity and thesimplicity (utility) of a noun phrase which refers to the entity. They also indicate correspondence
between the values of expected utility and the ranking of the transition states. These results indicatethat our generalization is appropriate.
1. Introduction
Principled and quantitative modeling of discourse is important for analyzing and generating
discourse. Centering theory (CT) is a model of discourse structures. It explains the relations among
attention, anaphora, and cohesion (Iida, 1997). However, CT has had two theoretical limitations.
The first is the lack of a general principle behind the discourse phenomena. Although some studies
on CT have focused on analyzing surficial linguistic features without general principles, weconsider that the principle of discourse phenomena must be addressed based on measurable
quantities. The second is that “salience”, which plays a critical role in CT, cannot be verified basedon large linguistic data because it is not formulated as a measurable quantity, but as heuristic rules.
We have investigated the general principle of CT. We adopted the meaning game (MG) (Hasida etal., 1995, 1996) framework because it gives a more principled explanation of the discourse
phenomena than CT does. MG is a model of intentional communication (e.g., anaphora) based on
game theory. Game players in game theory correspond to interlocutors in MG, and they decide theirintentions and interpretations at the Pareto-optimum. Although Hasida et al. (1995) claimed that
CT could be derived from the MG by formulating salience in terms of a reference probability, theirclaim has yet to be verified on the basis of substantial linguistic data. In this paper, we formulate theMG-based generalization of CT and verify it with a large corpus of Japanese newspaper articles.
Furthermore, we quantitatively define salience by using multiple regression with a corpus for the
MG-based generalization and for its verification.
2. Centering Theory and Its Two Issues
2.1 Centering Theory
In CT, a discourse is represented as a sequence of utterances [U1, U2, … ,Un]. The “center” is a
discourse entity which draws attention. The center is likely to be pronominalised. The “salience”
represents the degree of attention to a discourse entity. The salience also represents the likelihoodof pronominalization. The salience has been defined as a heuristic ranking in previous studies (seeSection 2.2). Centers are categorized as follows:¾ Cb(Ui): The backward-looking center of the utterance Ui, which denotes the most salient
discourse entity referenced in both the previous context and the current utterance Ui.
¾ Cf(Ui): The forward-looking centers of Ui, which denote a list of entities sorted by theirsalience.
¾ Cp(Ui): The preferred center of Ui, which is the most salient discourse entity in Cf(Ui).
CT embodies as the following rules (preferences) based on the heuristics definition of salience.
¾ Rule 1 (pronominalization): If any element in Cf(Ui) is pronominalized, the Cb(Ui) is also
pronominalized.
¾ Rule 2 (topic continuity): The transition states of centers between utterances (Table 1) are
preferred in the following order: CONTINUE > RETAIN > SMOOTH-SHIFT > ROUGHSHIFT.
Table 1: Transition states of centers between utterances
Cb(U i ) = Cb(U i −1 ) Cb(U i ) ≠ Cb(U i −1 )CONTINUESMOOTH-SHIFTCb(U i ) = Cp (U i )Cb(U i ) ≠ Cp (U i )RETAINROUGH-SHIFT

Rule 1 means that pronouns are more likely to refer to Cb than non-pronouns. Rule 2 represents thepreference order among transition states according to the strength of topic continuity.
2.2 Two Issues
Conventional CT studies face two limitations:1.
2.

Lack of principles behind the rules. CT does not explain why the two rules occur in discourse
phenomena.
Salience is formalized neither objectively nor quantitatively, but heuristically (e.g., Cf-ranking).
Such ranking is non-falsifiable (unscientific) and cannot be verified against real linguistic data.

The first limitation means that CT should have a hypothesis about the mechanisms behind
discourse phenomena. The second limitation means that CT should be based on the quantitative
definition of salience. Salience in CT is approximated by a heuristic ranking, called “Cf-ranking”(Walker et al., 1994), as follows:
English Cf-ranking: subject > object > indirect object > complement > adjunctJapanese Cf-ranking: topic (zero or grammatical) > subject > indirect object > object > others

Proceedings of PACLIC 19, the 19th Asia-Pacific Conference on Language, Information and Computation.

The above Cf-ranking depends on only grammatical function. While Strube et al. (1999) proposed
an extended Cf-ranking integrated with information status and Nariyama (2001) proposed an
extended ranking integrated with contextual information, these rankings are based on surficial
observations without sufficient theoretical grounds. Although Poesio et al. (2004) discussed theparameters settings in CT, their discussion was also based on heuristic ranking.
Besides this second limitation, we also note that heuristic ranking is difficult to integrate withother features that influence salience (e.g., distance between the current utterance and the latest
expression referring to the target entity).
We address the above two issues in the following sections.
3. Generalization of Centering Theory based on the Meaning Game
The meaning game (MG) is a hypothesis about a model of intentional communication based on
game theory (Hasida, 1996). We adopted MG to give CT a general principle. The MG-based
account of anaphora is a more principled hypothesis than that of CT, because MG is based on thegeneral principle of decision-making. In MG, the interlocutors’ expected utility is represented as:∑ Pr(e)Ut(w).

w refers to e

Here, the Pr(e) is the reference probability of a discourse entity e, which is the probability that e
will be referenced in the next utterance. Ut(w) is the utility of expression w that refers to e. The
lower the cost of speaking or hearing w is, the higher Ut(w) becomes. Here, we assume that thevalue of Pr(e) is shared by interlocutors. Under this assumption, the solution which provides the
maximum expected utility is the interlocutor’s Pareto-optimum because the expected utility isshared by them. We leave miscommunication out of consideration under that assumption.
Hasida et al. (1995) suggested that Rule 1 and 2 of CT can be derived from MG only in a few
particular cases.
3.1 Derivation of Preference 1a and 1b
Rule 1 of CT is a preference about pronominalization. Hasida et al. derived Rule 1 from MG in thefollowing case which involves little semantic bias, “he” tends to refer to “Fred”, and “the man” to“Max”.
U1: Fred scolded Max.
U2: He was angry with the man.
They assumed the following inequations in this case.
Pr(“Fred”) > Pr(“Max”)
Ut(“he”) > Ut(“the man”)(Q A subject is more salient than an object )(Q A pronoun costs less than a non-pronoun )In this case, the interlocutors have two choices of anaphora. Hasida et al. indicated the above
Table 2: Correspondence between MG and CT concepts
MGCT
Pr: Reference probability
Salience (Cf-ranking)High-Pr discourse entity
Center
Ut: Utility of noun phrase
Simplicity of noun phrase
High-Ut noun phrase
Pronoun
Low-Ut noun phrase
Non-pronoun

Choice (A)Choice (B)

Fred

Max

Fred

Max

“he”

“the man”“he”“the man”

Pr(“Fred”)Ut(“he”) + Pr(“Max”)Ut(“the man”) > Pr(“Fred”)Ut(“the man”) + Pr(“Max”)Ut(“he”)
Q (Pr(“Fred”) − Pr(“Max”)) (Ut(“he”) − Ut(“the man”)) > 0

Figure 1: Comparison of the expected utilities of two choices
Choice (A)Anaphors
high
a1
a2
low
Ut

Choice (B)Candidates ofAntecedent
highAnaphors
high

c1
c2

a1
a2

low
Ut

Candidates ofAntecedent
high
c1
c2

low
low
Pr
Pr
Pr(c1)Ut(a1)+Pr(c2)Ut(a2) > Pr(c2)Ut(a1)+Pr(c1)Ut(a2)Q (Pr(c1) − Pr(c2)) (Ut(a1) − Ut(a2)) > 0

Figure 2: Preference 1asemantic bias by comparing the expected utilities of the two choices. In other words, a solution of
their MG model is that choice (A) is preferred over choice (B) in Figure 1. This solution conforms
to a prediction using Rule 1. Thus, they claimed this thought experiment proves that rule 1 of CT
can be derived from MG. Table 2 shows correspondence between MG and CT concepts.
The above derivation, however, has neither been given a general formulation nor been verified on
the basis of substantial linguistic data. An utterance in general examples possibly has a few
anaphors and a lot of candidates of antecedent, whereas the above example case has only two
anaphors and only two candidates of antecedent. Thus, general formulation is required before one
can apply this model to real linguistic data. We generalize the above derivation to the following
preference.
Preference 1a: When an utterance has multiple anaphors, an anaphor with a higher utility among
them tends to refer to an entity with a higher reference probability.
Figure 2 illustrates Preference 1a we propose. In this example, choice (A) is preferred over choice(B). This is the preference in the cases of multiple anaphors in an utterance. Below, we generalize it
to cases that do not depend on the number of anaphors in an utterance as follows:
Preference 1b: There is a positive correlation between the utility and the reference probability.
These preferences are based on a general principle. Moreover, the coverage of these preferences iswider and more general than that of Rule 1 of CT. Accordingly, these preferences we propose are
generalizations of Rule 1.

Proceedings of PACLIC 19, the 19th Asia-Pacific Conference on Language, Information and Computation.

3.2 Derivation of Preference 2
Rule 2 of CT is a preference about local cohesion that indicates the level of topic continuity.
Transition states are categorized into four types with respect to two conditions (Table 1). These fourtypes have been heuristically ranked by local cohesion or topic continuity. The first condition,
Cb(Ui) =Cb(Ui−1), means that the current utterance Ui inherits Cb from the previous utterance Ui−1.
This condition corresponds to cohesion between Ui−1 and Ui. The second condition, Cb(Ui) =Cp(Ui),means that Cb(Ui) is the most salient entity in Ui . This condition corresponds to the prediction ofcohesion between Ui and Ui+1 because Cp(Ui), the most salient entity in Ui, is the most likely one tobe pronominalized in the following utterance Ui+1.
We consider that the preference order of Rule 2 is attributed to expected utility. When the first
condition holds, the reference probability of Cb is higher than when it does not hold. In this case,the utility of the anaphor referring to Cb also tends to become high because of Preference 1b, sothat the expected utility is high. Similarly, when the second condition holds, the reference
probability of Cb and the utility of Cb are high, thus, the expected utility is also high. Furthermore,
the first condition has stronger influence than the second, because the first one represents thecohesion between the previous and the current utterances, whereas the second merely predicts thecohesion between the current and the next utterances. Consequently, RETAIN has a larger expectedutility than SMOOTH-SHIFT. Rule 2 of CT can thus be derived from the general principle ofmaximum expected utility, which is stated as follows:
Preference 2: The interlocutors prefer an interpretation of anaphora with higher expected utility.
This preference is a generalization of Rule 2.
We will verify the above preferences and provide evidence of the existence of the MG principle
behind Rules 1 and 2 of CT in Section 5.
4. Definition and Measurement of Salience
Salience represents the likelihood of a discourse entity to be pronominalized or its degree ofattention. In CT, it is not quantitatively defined despite that it plays critical roles in the theory.
Therefore, we formulate salience in terms of a reference probability — a measurable quantity. The
salience of an entity can be defined based on how probable the entity will also be referenced in thefollowing utterances. In other words, if an entity seems to be referenced in the following discourse,
the entity tends to draw attention and its salience can be considered to be high. This formulation
resolves the issues of CT that were discussed in Section 2.
The salience of an entity e at the target utterance Ui is empirically defined as follows.
Definition of Salience: The salience of e at Ui is defined as the reference probability Pr(e, Ui),
which is the probability of e being referenced in the next utterance Ui+1. Given a large amount of
linguistic data, Pr(e, Ui) can be calculated as follows:
1. Find the latest reference to e in the previous discourse [U1, …, Ui]. Let it be we.
2. Compose the feature vector feat(we,Ui) from we and [U1, …, Ui] . For example, the features weused in this study are listed in Table 3.
3. Extract samples (wx,Uj) whose feature vectors feat(wx,Uj) equal feat(we,Ui) from a large amountof linguistic data.
4. Using the extracted samples, calculate Pr(wx, Uj), the probability that the referent of wx is also
referenced in Uj+1 (in other words, calculate the relative frequency of samples that the referentof wx is also referenced in Uj+1).
5. Take Pr(wx, Uj) to be Pr(e, Ui).

Table 3: Features used in regression analysis of Pr(e,Ui)
(1)

(2)

Dist
Gram
Chain
Exp
last_topic
last_sbjp1
Poslog ( (# utterances between Ui and the latest reference to e ) + 1)
grammatical function of the latest reference to e (wa/ga/no/o/ni/mo/de/kara/to)log ( (# references to e in the previous context of Ui) + 1)
expression type of the latest reference to e (pronoun/non-pronoun)
whether the latest reference to e was the last topic (yes/no)whether the latest reference to e was the last subject (yes/no)whether e was in the first person (yes/no)part of speech of the latest reference to e

We used (1) for MLR, and (1) and (2) for SVR.
This definition is expressed by the following equation.
(Salience of e at Ui) := Pr(e, U i ) ≈ Pr( wx , U j ) =# {( w x , U j ) ; C ∧ D}
# {( wx , U j ); C}

Condition C: feat(wx,Uj) = feat(we, Ui)
Condition D: The referent of wx is also referenced in Uj+1.
Hereafter, we explain the measurement of the salience of “Tom” at Ui for the following example.
U i-2: I saw Tom a little while ago.
U i-1: He seems to be sleepy.
U i : It was so hot last night,.
Pr(“Tom”,Ui)
U i+1:In this example, the anaphor “he” refers to “Tom” and it appears in the last position among
expressions referring to “Tom” in the previous discourse. We call it the latest reference to “Tom”.
To simplify the explanation, if the following three features are used, feat(“Tom”,Ui) is defined as(dist = 2, gram =subject, chain = 2).
¾ dist : Utterances between Ui and the latest reference to e.
¾ gram : Grammatical function of the latest reference to e.
¾ chain : References to e in the previous context of Ui
We extract samples (wx,Uj) that have the same feature vector as feat(“Tom”,Ui) from a corpus andcalculate the reference probability from these samples.
U j-k:….
U j-1:Uj :U j+1:

.
wx

.
.
.

Condition C: feat(wx,Uj) = feat(“Tom”,Ui)
Condition D: The referent of wx is also referenced in Uj+1.
Pr(“Tom”,Ui) ≈ Pr( w x , U j ) =# {( w x , U j ) ; C ∧ D}
# {( w x , U j ); C}

Notice that interpolation and extrapolation are necessary because of data sparseness in the corpus.
To this end, we used regression analysis for the measurements. We measured the reference
probability with two regression algorithms: MLR (multiple logistic regression) and SVR (support
vector regression). Table 3 lists the features for regression in this study.

Proceedings of PACLIC 19, the 19th Asia-Pacific Conference on Language, Information and Computation.

5. Empirical Verification of Meaning-Game-based Generalization
We statistically verified Preference 1a, 1b, and 2 derived from MG. We used 1,356 articles takenfrom Japanese newspapers annotated with Global Document Annotation (GDA) (Hasida, 1998).
These articles contained 63,562 utterances (predicate clauses). Table 4 shows the distribution ofanaphora types in the corpus. To measure the reference probability, we extracted 1,073,781 samples
of previously referenced entities for each utterance. Table 5 shows that there were 16,728 pairs ofan utterance Ui and a previously referenced entity e that is also referenced in Ui (namely, that
corpus contains 16,728 anaphors).
Table 4: Distribution of Japanese anaphora types
Anaphora Types# Sample Ratio
Zero Pronoun
5876
35.1%
Pronoun843
5.0%
Noun Phrase with Demonstrative
1011
6.0%
Other Noun Phrase
8998
53.8%
Total
16728 100.0%
Table 5: Percentage of samples in which previously referenced e is also referenced in Ui# Sample (e, Ui) Percentage
e is referenced in Ui
16,728
1.6%
e is not referenced in Ui
1,057,053
98.4%
Total
1,073,781
100.0%
We assumed that the utility of pronouns is greater than that of non-pronouns; i.e., the utility ofpronouns equals 2, and that of non-pronouns equals 1. This assumption is equivalent todistinguishing between pronouns and non-pronouns in CT.
5.1 Measurement of Salience as Reference Probability
We measured reference probability, which is required in the verification of our MG-based
generalization in Section 5.2. We used two regression algorithms for the measurement: MLR and
SVR, which will be mentioned in Section 5.1.2 and 5.1.3, respectively. These regressions,especially MLR, require that their features must be numeric values. However, a grammatical
function is not defined as numeric values. Therefore, we assigned numeric values to theTable 6: Reference probabilities by only
Japanese grammatical functions (by particles)
Referenced Reference
Particle# Samplein Ui+1(Grammatical Function)
Probabilitywa (topic)
35,3291,908 0.0540
ga (subject)
38,4501,107 0.0288
no (of)88,695
1,755 0.0198
o (direct object)
50,217898 0.0179
ni (indirect object)
46,058569 0.0124
mo
8,710
105 0.0121
de24,142267 0.0111
kara
7,963
76 0.00954
to19,383129 0.00666
Other particles
512,006
8,027 0.0157
No particle
153,197
1,315 0.00858

grammatical functions as a preparation for the multiple regressions in Section 5.1.1.
After these regressions, we will also reconsider the conventional Japanese Cf-ranking based on theassigned values for grammatical functions in Section 5.1.4.
5.1.1 Assigning Numeric Values to Grammatical Functions
We measured the reference probabilities by using only grammatical functions for enabling theregression. This preparative measurement involves not regression but counting samples. Table 6
shows the reference probabilities calculated by from only the grammatical functions existing in the
corpus. We used these values as gram in the multiple regression of the reference probability.
5.1.2 Measurement with MLR
MLR model is based on an assumption that the log odds of probability, log(P (1 − P)) , of somekind of event can be expressed as a linear expression of the explanatory variables. The regressionfunction with three features in Table 3 is
Pr = (1 + exp(−λ )) −1= (1 + exp( −(b0 + b1 dist + b2 gram + b3 chain ))) −1 .
It takes a huge amount of time to perform MLR on 1,073,781 samples. Thus, we made fiveregression models using 12,000 subsamples per model. We used statistical software called R (RDevelopment Core Team, 2002) for the MLR analysis. Table 7 shows the parameters of the fiveregression models. We used average of probabilities predicted by the five models as the reference
probability, which is represented as follows:
Pr =

1 5
(1 + exp( −(bk , 0 + bk ,1 dist + bk , 2 gram + bk ,3 chain ))) −1∑
5 k =1

Table 7: Measured parameters of the five MLR models
bk,0
bk,1
bk,2
bk,3
k: Model No.
(coeff. of dist)(coeff. of gram)(coeff. of chain)(const.)1-2.825-0.7636
9.036
2.048
2
-3.055-0.7067
10.47
2.270
3
-2.952-0.7574
6.433
2.399
4
-3.288-0.5911
9.170
2.129
5
-3.043-0.6578
4.836
2.178
Measurement with SVR
We also made an SVR model to measure the reference probability with the eight features listed inTable 3. In MLR, the input values of the target variable are 0 or 1. However, in SVR, the input
values must be smoothed as real numbers. We subsampled 60,000 samples, smoothed the input
variables by using the k-NN method with k =100, and made an SVR model of a 2nd-degree
polynomial kernel by using TinySVM (Kudo, 2002).

5.1.3

Reconsideration of Conventional Japanese Cf-ranking
Notice that the direct object is higher ranked than the indirect object in Table 6. This order is
opposite from the conventional Japanese Cf-ranking order (Kameyama, 1998, Walker et al., 1994).
Unfortunately, we have no way of telling which order is right from only this result.
To verify the order of the direct and indirect objects in Japanese, we need to consider another view
point. To set the other ranking for this purpose, we calculate coefficients of linear regression of an

5.1.4

Proceedings of PACLIC 19, the 19th Asia-Pacific Conference on Language, Information and Computation.

anophor’s utility (in the next utterance) by using only grammatical functions (in the current
utterance) in the corpus. These coefficients are assigned to each grammatical function for
maximizing the correlation between them and utilities of noun phrases. In other words, they can be
regarded as rigged values to maximize the predictive ability of Preferences 1a and 1b. Table 8 lists
these coefficients and their ranking among the grammatical functions. This result also indicates thatthe direct object is higher ranked than the indirect object. Consequently, these empirical results
disprove the order of direct and indirect objects in the conventional Japanese Cf-ranking.
Table 8: Coefficient for maximizing correlation to Ut
Particle (Grammatical Function) Coefficientwa (topic)
5.46
mo
5.37
ga (subject)
5.27
kara
5.14
o (object)
5.12
to
5.05
ni (indirect object)
5.05
no (of)
5.04
de
4.98
5.2 Empirical Verification of MG-based Generalization

We statistically verified Preferences 1a, 1b, and 2 using the reference probabilities obtained in
Section 5.1.
5.2.1 Verification of Preference 1a and 1b
Firstly, we made pairs of anaphors in the same utterance for verifying Preference 1a. There were
914 pairs in utterances having multiple anaphors (Table 9). There were 360 pronoun and nonpronoun pairs. Thus, we calculated the percentage of samples that agreed with the prediction of
Table 9: Distribution of anaphor number in the same utterance
Anaphors
in a same utterance

0
1
2
3
Total

MLR

SVR

Pairs of anaphors

Utterances

Anaphors

47,728
14,960854
2063,562

14,9601,708
60
16,728Percentage in the same utterance
89.4%
10.2%
854
0.4%
60
100.0%
914

Table 10: Verification of Preference 1a and 1b
Measured 95% Confidence Interval
Preference 1a: Agreement Percentage
75.3%[70.5, 79.6](in 360 pairs of anaphor)(271/360)
Preference 1b: Correlation Coefficient(in 16,728 samples)
Preference 1a: Agreement Percentage(in 360 pairs of anaphor)
Preference 1b: Correlation Coefficient(in 16,728 samples)+0.373[0.360, 0.386]

74.4%(268/360)[69.6, 78.9]+0.386[0.373, 0.399]

Preference 1a from these 360 pairs. We assumed that the percentage was binomially distributed andcalculated the 95% confidence interval of the percentage. Table 10 shows that at least 70% of thesamples agreed with Preference 1a.
Secondly, to verify Preference 1b, we measured Pearson’s correlation coefficient between
reference probability and utility. We assumed that the correlation coefficient was t-distributed andcalculated the 95% confidence interval. Table 10 shows that the correlation coefficient ofPreference 1b was at least +0.36 in both MLR and SVR. These results show that Preferences 1a and1b were verified with statistical significance.
5.2.2 Verification of Preference 2
Table 11 shows the distribution of transition states in the corpus (decision on centers based onreference probabilities estimated by MLR as salience values). We see that the frequency of
RETAIN is low despite its high preference rank. This tendency of the paucity of RETAIN has also
been observed by Iida (1997) and Yamura-Takei et al. (2000). We cannot assume that thepreference order matches the frequency order because the four transition states can not always be
selected for every utterance.
Table 12 shows the averages and variances of the expected utility for each transition state. The
order of the data in the table conforms to the order of Rule 2 of CT. We tested this order withmultiple comparison tests. The results of the Kruskal-Wallis test were χ 2 = 1780.7, df = 3, and P< 2.2 × 10 −16 . This means that the averages of the four states differed significantly. Table 13 shows
the result of the Wilcoxon’s rank sum test using the method of Holm, which demonstrates that theorder is statistically significant. Additionally, the correlation coefficient between the transition
states and the averages of expected utility in Table 12 was +0.520 when we assigned the following
Table 11: Distribution of transition states
Zero Pronoun
PronounTotal of Pronoun
Noun Phrase with Dem.
Other Noun Phrase
Total of Non-Pronoun
Total of All

CONTINUE
56.0%(1315/2347)
43.6%(102/234)
54.9%(1417/2581)
20.9%(56/268)
20.0%(522/2611)
20.1%(578/2879)
36.5%(1995/5460)

RETAIN
1.7%(41/2347)
2.1%(5/234)
1.8%(46/2581)
3.0%(8/268)
1.8%(48/2611)
1.9%(56/2879)
1.9%(102/5460)

SMOOTH-SHIFT
38.3%(898/2347)
50.9%(8/234)
39.4%(1017/2581)
64.2%(172/268)
67.4%(1761/2611)
67.1%(1933/2879)
54.0%(2950/5460)

ROUGH-SHIFT
4.0%(93/2347)
3.4%(8/234)
3.9%(101/2581)
11.9%(32/268)
10.7%(280/2611)
10.8%(312/2879)
7.6%(413/5460)

Table 12: Averages of expected utilities in each transition states
Transition State#Sample Ave. of Expected Utility (Their Variance)
CONTINUE
0.874(0.361)
1,995
RETAIN
0.473(0.242)102
SMOOTH-SHIFT
0.287(0.175)2,950
ROUGH-SHIFT
0.109(0.0336)
413
Table 13: Wilcoxon’s rank sum test
Pair of Transition States for Comparison
Significance Probability
CONTINUE : RETAIN
5.89 × 10−13
CONTINUE : SMOOTH-SHIFT< 2.2 × 10−16
CONTINUE : ROUGH-SHIFT< 2.2 × 10−16
RETAIN : SMOOTH-SHIFT
1.64 × 10−6
RETAIN : ROUGH-SHIFT< 2.2 × 10−16
SMOOTH-SHIFT : ROUGH-SHIFT< 2.2 × 10−16

Proceedings of PACLIC 19, the 19th Asia-Pacific Conference on Language, Information and Computation.

values: CONITNUE=4, RETAIN=3, SMOOTH-SHIFT=2, ROUGH-SHIFT=1. This means that
expected utility correlates with topic continuity.
These results provide statistical evidence of a principle of the Meaning Game behind Rules 1 and
2 in Centering Theory.
6. Discussion
6.1 Effect of Quantitative Definition of Salience as the Reference Probability
We resolved the problems regarding salience in Section 2 by formulating it as a reference
probability. That is,¾ In our formulation, salience becomes a measurable quantity and becomes statistically verifiable
based on large linguistic data.
¾ By adopting regression algorithms that can handle multiple explanatory variables, the model
can more easily integrate features that influence salience than heuristic methods of previous
works.
¾ By taking into account the distance between the current utterance and the latest references toentities, the model can handle not only entities referenced in the previous utterance but also all
entities in the previous discourse.
6.2 Samples Disagreeing with Preference 1a
In Section 5.1.1, we confirmed that 75.3% of samples favored Preference 1a with MLR and that
74.4% samples favored it with SVR. This means, however, that about 25% of samples did not favor
Preference 1a. In checking the results, we found that semantic features (e.g., selectional restrictionof predicate, semantic category of anaphor, and so on.) accounted for this difference. We consider
that if these features were imported to the multiple regression of the reference probability,
Preferences 1a and 1b would become even stronger.
6.3 Strictness of Verification of Preference 2
In Section 5.2.2, we verified the correspondence between the order of averages expected utility foreach transition state and the order of Rule 2 of CT. This means that Rule 2 of CT can be derived
from MG. This verification is, however, not always strict. We should verify the order of thesolutions of each case, not the order of the averages. We leave this issue as a future work.
7. Conclusion
CT has two limitations despite it being a standard theory about discourses. It lacks a principle
behind discourse phenomena and a quantitative definition of salience. We have quantitatively
formulated salience as a reference probability from the standpoint that the principle underlying
discourse can be attributed to game theory. Furthermore, we formulated two preferences as the MGbased generalization of CT and statistically verified these preferences in a Japanese corpus.
In our verification of Preference 1a and 1b, we claimed that there is a positive correlation between
the utility of an anaphor and the reference probability of its referent. In connection with this, theconventional Japanese Cf-ranking was empirically disproved. Preferences 1a and 1b derived from
MG cover more general cases than Rule 1 in CT does. In our verification of Preference 2, weestimated the average expected utility for the four transition states and presented evidence that theorder among the averages corresponds to that of Rule 2 in CT. These empirical results indicate thata principle informed by MG is behind both rules in CT.
We hence conclude that we have statistically proved our MG-based generalization. It is a morequantitative and principled model than conventional CT.

8. Acknowledgements
The authors are grateful to members of the now-defunct Cyber Assist Research Center and thepeople who annotated the GDA tags to the corpus used in our study.
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